Category: mathematics

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What’s seven times nine? Quick, you’ve got six seconds to answer.

This June, over 600,000 children in England in year four, aged eight and nine, will be expected to answer questions like this. They will be sitting the multiplication tables check (MTC), a statutory assessment of their multiplication fact recall.

The MTC was introduced in 2022 with the aim of driving up standards in mathematics. It’s an online test that children take on a tablet or computer, made up of 25 questions with six seconds per question.

Being able to quickly recall multiplication facts is valuable. Not having to think about seven times nine, just knowing that it’s 63, frees up a child’s mental thinking space. This means they can focus on different aspects of the mathematics they are doing, such as completing multi-step problems or using reasoning to solve context-based problems.

Being able to quickly recall multiplication facts is also the foundation for more advanced mathematics topics that children will encounter at secondary school.

Our research shows that the MTC is an accurate reflection of children’s multiplication fact recall. But the learning they do for this test doesn’t necessarily help them apply this knowledge in other areas of mathematics. What’s more, focus on the MTC may be diverting teaching time away from other maths knowledge.

Since the multiplication tables check was introduced in 2022, the average score in the test has increased year-on-year from 19.8 in 2022 to 20.6 in 2024. This suggests that schools are placing more emphasis on children’s multiplication fact recall – and on preparing them for this test.

Teaching union the NAHT (National Association of Head Teachers) has suggested that the test is unnecessary, and that it places too much emphasis on fact recall at a cost to other areas of mathematics. The union has also expressed concerns that it disadvantages some children for reasons such as digital accessibility.

Our research has investigated whether the MTC is a good way of testing children’s recall of multiplication facts. We have found that children perform just as well on a more traditional paper-and-pencil timed fact test as on a computer test equivalent to the MTC. However, having a time limit per question – which is only possible with a computerised test – is essential to assess recall, rather than fast calculation.

Pupils taking part in the research project. Lisa Gilligan-Lee/University of Nottingham, Author provided (no reuse)

There was no evidence that any children were particularly disadvantaged by the computerised test. However, we did find that children’s attention skills and how quickly they could enter numbers into the tablet they were using did influence their scores.

This suggests that, for it to be a fair test, it is important that children are familiar with the technology they are using to complete the test. Given that there are stark differences in access to technology in schools, this may pose an issue for some children.

The purpose of introducing the MTC was to improve children’s broader mathematics attainment by improving their multiplication fact recall. But performance in the year six Sats tests, which assess a range of mathematical skills, shows little change.

Crucially, improving children’s multiplication fact recall through retrieval practice doesn’t equate to improving their ability to use the multiplication facts they know. If posed a question such as “Tara has seven books. Ravi has four times as many. How many books do they have altogether?” Children who can recall that 5 x 7 = 35 may still not be able to solve the problem.

Time pressure

What’s more, because the MTC is a timed test, teachers and parents may use similar time-pressured approaches to prepare children and help them improve their multiplication fact recall. But our research showed that while practice with a computerised game can support children’s fact recall, the benefits to learning are the same whether or not children are encouraged to answer as quickly as possible.

In research not yet published in a peer-reviewed journal, we found that children who were anxious about mathematics learnt less when practising with time pressure compared to children without mathematics anxiety. Without time pressure, anxiety levels were not related to the amount of learning. Doing some regular multiplication fact retrieval practice is more important than the type of practice, for all learners.

Even though the MTC is a timed assessment, it doesn’t mean that children only need to do timed practice to prepare for this. Some children may benefit more from less time pressure when practising.

Multiplication fact recall is just one element of mathematics and so having a good balance is important. Fact recall and testing should go hand in hand with other areas of mathematics learning such as understanding concepts, choosing strategies and solving applied problems.

Recalling multiplication facts doesn’t automatically help children to apply their knowledge. So, although working towards the multiplication tables check can support fact recall, children will need extra support in knowing how to use and apply these facts.

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Camilla Gilmore, Lucy Cragg & Natasha Guy*

 

Sydney Bourne/ AAP

If you ask a small child a simple maths question, such as 4+2, they may count on their fingers to work it out.

Should we encourage young children to do this? This seemingly simple question is surprisingly complex to answer.

Some teachers and parents might say, yes, it seems to help young children learn about numbers. Others might discourage finger counting, arguing it might slow the development of mental strategies.

A new Swiss study, released on Friday, shows kids who use finger counting from a young age perform better at addition than those who do not.

What does the research say?

There is a rich debate among researchers about the value of kids using their fingers to count.

Education psychologists say finger counting helps children think through strategies without overloading their working memory (how our brains hold pieces of information for short time while we work something out), until more abstract strategies are mastered.

Researchers in embodied cognition (learning through actions) argue associating fingers and numbers is “doing what comes naturally” and so, should be encouraged. Neuroscientists might also note similar parts of your brain activate when you move your fingers and think about numbers, which helps memory.

Several previous classroom studies have shown children who use finger strategies to solve maths questions perform better than children who do not, until around seven when the opposite becomes true.

So, before age seven, finger-counters are better. After seven, non-finger-counters are better.

Why does this happen? What does this mean for mathematics education? This has been a point of debate for several years.

A new study followed 200 kids

A new University of Lausane study has taken an important step in settling this debate.

The researchers say previous studies have left us with two possible explanations for the apparent change in the benefits of finger counting at about seven.

One interpretation is finger strategies become inefficient when maths questions become more complex (for example 13 + 9 is harder than 1 + 3), so children who use finger strategies don’t perform as well.

The other possibility is the children who are not using finger strategies at seven (and performing better than those who do) were previously finger-users, who have transitioned to more advanced mental strategies.

To untangle these contrasting explanations, the researchers followed almost 200 children from age 4.5 to 7.5 and assessed their addition skills and finger use every six months.

Notably, they tracked if and when the children started and stopped using their fingers. So, at each assessment point, it was noted whether children were non-finger users, new finger-users (newly started), continuing finger-users, or ex-finger users (had stopped).

What did the study find?

The study found that by 6.5 years most of the non-finger users were indeed ex-finger users. These ex-finger users were also the highest performers in the addition questions and were still improving a year later. The significance of this finding is that in previous studies, these high performing children had only been identified as non-finger users, not as former users of finger-based strategies.

In the new Swiss study, only 12 children never used their fingers over the years, and they were the lowest performing group.

Additionally, the study showed the “late starters” with finger-counting strategies, who were still using finger strategies at the age of 6.5 to 7.5 years, did not perform as well as the ex-finger users.

What does this mean?

The findings from this unique longitudinal study are powerful. It seems reasonable to conclude both teachers and parents should encourage finger counting development from preschool through the first couple of years of school.

However, the Swiss study focused on predominantly white European children from middle to high socioeconomic backgrounds. Would we find such clear outcomes in the average multicultural public school in Australia? We suspect that we might.

Our own 2025 study found a wide variety of finger counting methods in such schools, but when teachers paid attention to the development of finger counting strategies it supported children’s number skills.

What can parents do?

Parents can show preschoolers how they can use their fingers to represent numbers, such as holding up three fingers and saying “three”.

Help them practice counting from one to ten, matching one finger at a time. Once they get started, the rest should come naturally. There is no need to discourage finger counting at any time. Children naturally stop using their fingers when they no longer need them.

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Jennifer Way & Katherin Cartwright*

Despite using numerical bases on a daily basis, few of us have reflected on the nature of these cognitive tools. (Getty Images/Unsplash+)

Most of us have little trouble working out how many millilitres are in 2.4 litres of water (it’s 2,400). But the same can’t be said when we’re asked how many minutes are in 2.4 hours (it’s 144).

That’s because the Indo-Arabic numerals we often use to represent numbers are base-10, while the system we often use to measure time is base-60.

Expressing time in decimal notation leads to an interaction between these two bases, which can have implications at both the cognitive and cultural level.

Such base interactions and their consequences are among the important topics covered in a new issue of the Philosophical Transactions of the Royal Society journal, which I co-edited with colleagues Andrea Bender (University of Bergen), Mary Walworth (French National Centre for Scientific Research) and Simon J. Greenhill (University of Auckland).

The themed issue brings together work from anthropology, linguistics, philosophy and psychology to examine how humans conceptualize numbers and the numeral systems we build around them.

What are bases, and why do they matter?

Despite using numeral bases on a daily basis, few of us have reflected on the nature of these cognitive tools. As I explain in my contribution to the issue, bases are special numbers in the numeral systems we use.

Because our memories aren’t unlimited, we can’t represent each number with its own unique label. Instead, we use a small set of numerals to build larger ones, like “three hundred forty-two.”

The degree to which numeral systems transparently reflect their bases has all sorts of implications. (Pablo Merchán Montes/Unsplash+)

That’s why most numeral systems are structured around a compositional anchor — a special number with a name that serves as a building block to form names for other numbers. Bases are anchors that exploit powers of a special number to form complex numerical expressions.

The English language, for example, uses a decimal system, meaning it uses the powers of 10 to compose numerals. So we compose “three hundred and forty-two” using three times the second power of 10 (100), four times the first power of 10 (10) and two times the zeroth power of 10 (one).

This base structure allows us to represent numbers of all sizes without overloading our cognitive resources.

Languages affect how we count

Despite the abstract nature of numbers, the degree to which numeral systems transparently reflect their bases has very concrete implications — and not just when we tell time. Languages with less transparent rules will take longer to learn, longer to process and can lead to more calculation and dictation errors.

Take French numerals, for example. While languages like French, English and Mandarin all share the same base of 10, most dialects of French have what could politely be called a quirky way of representing numbers in the 70-99 range.

Seventy is soixante-dix in French, meaning “six times 10 plus 10,” while 80 uses 20 as an anchor and becomes quatre-vingts, meaning “four twenties” (or “four twenty,” depending on the context). And 90 is quatre vingt dix, meaning “four twenty ten.”

French is far from being alone in being quirky with its numerals. In German, numbers from 13 to 99 are expressed with the ones before the tens, but numbers over 100 switch back to saying the largest unit first.

Even in English, the fact that “twelve” is said instead of “ten two” hides the decimal rules at play. Such irregularities spread far beyond languages.

How bases shape learning and thought

Base-related oddities are spread out across the globe and have very real implications for how easily children learn what numbers are and how they interact with objects such as blocks, and for how efficiently adults manipulate notations.

For example, one study found that lack of base transparency slows down the acquisition of some numerical abilities in children, while another found similar negative effects on how quickly they learn how to count.

A young boy learns counting on an abacus at a school in Allahabad, India, in 2015. (AP Photo/Rajesh Kumar Singh)

Another study found that children from base-transparent languages were quicker to use large blocks worth 10 units to represent larger numbers (for example, expressing 32 using three large blocs and two small ones) than children with base-related irregularities.

While Mandarin’s perfectly transparent decimal structure can simplify learning, a new research method suggests that children may find it easier to learn what numbers are if they are exposed to systems with compositional anchors that are smaller than 10.

In general, how we represent bases has very concrete cognitive implications, including how easily we can learn number systems and which types of systems will tend to be used in which contexts.

Technicians lower the Mars Climate Orbiter onto its work stand in the Spacecraft Assembly and Encapsulation Facility-2 in 1998. (NASA)

At a cultural level, base representation influences our ability to collaborate with scientists across disciplines and across cultures. This was starkly illustrated by the infamous Mars Climate Orbiter incident, when a mix-up between metric and imperial units caused a $327 million spacecraft to crash into Mars in 1999.

Why understanding bases matters

Numeracy — the ability to understand and use numbers — is a crucial part of our modern lives. It has implications for our quality of life and for our ability to make informed decisions in domains like health and finances.

For example, being more familiar with numbers will influence how easily we can choose between retirement plans, how we consider trade-offs between side-effects and benefits when choosing between medications or how well we understand how probabilities apply to our investments.

And yet many struggle to learn what numbers are, with millions suffering from math anxiety. Developing better methods for helping people learn how to manipulate numbers can therefore help millions of people improve their lives.

Research on the cognitive and cultural implications of bases collected in the Philosophical Transactions of the Royal Society journal can help make progress towards our understanding of how we think about numbers, marking an important step towards making numbers more accessible to everyone.

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Jean-Charles Pelland*

 

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If the recent news of a new mathematics and statistics curriculum for years 0–10 felt familiar, that’s because it was.

In term four last year, the Ministry of Education released a previous new maths (and English) curriculum for Years 0–8, to be implemented from term one this year.

Schools must use the latest new curriculum from term one next year. This will be the third curriculum for primary and intermediate schools in less than three years.

Despite claims that the most recent curriculum is only an “update”, the changes are bigger than teachers might have expected.

The new curriculum is more difficult and more full. There is now a longer list of maths procedures and vocabulary to be memorised at each year of school.

For example, year 3 children should learn there are 366 days in a leap year and that leap years happen every four years. Year 5 students should know what acute, obtuse and reflex angles are.

Some concepts have been moved into earlier years. Year 6 children will learn calculations with rational numbers (such as “75% is 24, find the whole amount”), whereas previously this would have been taught at year 8. (If you’re wondering, the whole amount is 32.)

Cubes and cube roots have been moved a year earlier. A lot of statistics, a traditional area of strength for New Zealand in international tests, has been stripped out.

Much of the “effective maths teaching” material about clearly explaining concepts and planning for challenging problem solving has been removed. Also gone are the “teaching considerations” that helped guide teachers on appropriate ways to teach the content.

The maths children should learn was previously broken up into what they needed to “understand, know and do” – the UKD model. But this has changed to “knowledge” and “practices”.

In short, there are new things to teach, things to teach in different years, and the whole curriculum is harder and structured differently. It is effectively a new curriculum.

Not just a document

Most teachers now have about eight school weeks to plan for the changes, alongside teaching, planning, marking, reporting, pastoral support and extracurricular activities.

For busy schools heading into the end of the school year, the timeline is unrealistic, some say a “nightmare”.

For secondary teachers, who will be making changes in years 9 and 10, this is the first major curriculum change since 2007.

Primary and intermediate teachers, who have worked hard this year getting up to speed with a new curriculum that will soon expire, might legitimately ask why they bothered.

A curriculum change is a big deal in a school, something that normally happens once in a decade or more. A curriculum is not just a document, it is used every day for planning, teaching and assessment. Any change requires more lead time than this.

 

When England launched a new National Curriculum in 2013, teachers had it 12 months ahead of implementation. Singapore, a country whose education system Education Minister Erica Stanford paints as exemplary, gave teachers two years to prepare for the secondary maths curriculum change in 2020.

Expecting teachers to prepare for major curriculum changes in eight weeks is not only unnecessarily rushed and stressful – it is also a risk to children’s learning.

Time to slow down

Term one next year also marks the implementation of the new “student monitoring, assessment and reporting tool” (SMART) which teachers have not yet seen.

Children in Years 3–10 will take maths tests twice a year and will be described as emerging, developing, consolidating, proficient or exceeding. Children in the top three categories (during the year) or top two categories (at the end of year) are “on track”.

For the rest, the curriculum says “teachers will need to adjust classroom practice, develop individualised responses, or trigger additional learning support”.

The original curriculum rewrite shifted the goalposts – only 22% of year 8 students would be at the “expectation” level, compared with 42% previously – and this curriculum shifts those goalposts further.

The inevitably poorer results from testing against a more challenging curriculum risk damaging children’s self confidence, disappointing parents and placing blame on teachers.

Test results may improve in later years, compared to those produced in the first year of assessment against a harder curriculum that will take time to embed. But that will not necessarily be evidence the change was justified.

Pausing this latest curriculum change for at least 12 months would give time for adequate consultation and preparation. That would be more consistent with the change processes of education systems internationally.

According to a recent report from the Education Review Office, teachers have mostly demonstrated professionalism in their conscientious adoption of the previous curriculum.

In our view, the most recent changes will severely test that goodwill.

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to David Pomeroy & Lisa Darragh*

Black ice/ Pexels , CC BY

Mathematics has been the broccoli of school subjects for generations of Australian teenagers.

Often pushed aside, dreaded, or even feared, nearly one third of students opt out of any senior maths courses.

This has serious implications for Australia’s future. As an Australian Academy of Science report warned on Thursday, we need people with maths skills to support a whole range of careers in science. This includes agricultural science, artificial intelligence, data science, biotechnology and climate science.

The skills we gain during school mathematics – problem-solving, pattern-finding, reasoning logically, and computational thinking – are essential to the work of many STEM careers.

The challenge is turning maths from broccoli to the ingredient every student wants on their plate for their future. So, what can we do?

What has been happening with high school maths?

Across Australia, there has been a decline in students studying maths in years 11 and 12 since the 1990s. Today, only 8.4% of Australian high school students study the most difficult level of maths.

There are diverse reasons explaining why students opt out of maths during school.

Many students struggle to see the relevance of the maths they are learning for their future. Others have low self-confidence and avoid maths, believing they are not capable. An increasing range of senior subjects has also led to students being drawn to more enticing alternatives.

What can parents do?

Research shows parents’ attitudes towards maths can predict the attitudes their children will have towards the subject.

This means we need to be careful as parents. If we have negative attitudes towards maths due to our own anxieties or past struggles, this can affect our children’s attitudes and performance too.

Instead, parents should try to focus on the positive aspects of maths.

For example, this is a subject where you learn about the mechanics of the world, rather than a subject to be endured before moving to the “fun” stuff. Maths can come alive once we notice how we use it in sports, art, cooking, travel, money management and games.

Parents can also be curious co-learners with their children – we never need to have all the answers ourselves. But showing interest, having a growth mindset (a belief you can improve your abilities through effort), and asking questions can support students’ positive attitudes and performance in maths.

You can also talk to your child about why mastering maths is central to a wide range of occupations, from coding to trades, retail, nursing, animation and architecture.

What should schools do?

Research suggests 20% of 15-year-old boys and 33% of 15-year-old girls do not think maths will be relevant to their future.

So we need a new approach to careers advice in schools. Students need adequate support from informed adults to make accurate judgements about career pathways – emphasising how maths can help.

On top of this, schools could consider the ways in which mathematics is celebrated and promoted in schools. While music, drama, and sport days are regular features of the school calendar, maths is rarely included. Exciting maths competitions and maths days are prime opportunities to show students how important maths is in our world.

What about teachers?

Some of us may remember maths lessons as rather dry with a focus on lots of questions and whether something was “wrong” or “right”.

So teachers who make maths engaging for students and maximise opportunities for success are crucial.

This involves making abstract mathematics real (how does this concept apply to something physical in the real world?).

Teachers should also provide step-by-step support to students (what educators call “scaffolding”), so young people experience a sense of achievement and success with maths. Success builds motivation, creating an upward spiral of positive maths experiences.

What can governments do?

The alarm bells over maths participation have been raised for 30 years, with government funding supporting research into this phenomenon.

Despite this, the declines persist, and gender gaps in maths have widened, with more boys doing maths and more boys achieving higher marks.

So while governments should continue to support research into this matter, they should prioritise translating it into practical strategies for schools and teachers.

Some evidence-based approaches include:

high-expectation teaching, where teachers set ambitious goals, create supportive classrooms, and believe all students can achieve

relevance interventions, where teachers show students the practical implications of their learning

mindset interventions, which help students believe in their abilities.

Getting kids back into maths

Maths participation is both a national concern and something we should all be personally attuned to.

The lifestyles of future generations will be dependent on our capacity to be STEM innovators.

At an individual level, when students opt-out of mathematics, they are potentially closing many doors in their lives and career.

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Bronwyn Reid O’Connor & Ben Zunica*

 

When Grade 5 teacher Jared Bremner joined First Baptist Christian School in the Cayman Islands, Mathletics was already woven into their math curriculum.

Six years later, he can’t imagine teaching without it.

First Baptist’s approach was different from the start: they were intentional about implementation. What started as simply adding another digital resource has become a complete shift in how students experience math from Kindergarten through Grade 8.

Mathletics, our ESSA-certified online math program for ages 5–16, delivers personalized learning through explicit and systematic instruction, engaging activities, gamified challenges and immediate feedback. But at First Baptist, it’s become much more than a supplement: it’s central to how they teach.

Bremner now oversees implementation across the entire school, ensuring every new teacher successfully integrates the program into their lessons.

His personal journey, from newcomer to passionate champion, reflects the school’s own evolution in digital math education.

From ‘just another resource’ to essential instruction

Six years ago, First Baptist had a clear goal: find a math platform with diverse resources that teachers could actually use to improve instruction through technology.

“While it started off as just a resource they wanted to use,” Bremner reflects, “is now an important part of our instruction.” What made the difference? “We find Mathletics to be very encompassing. It’s a very layered product,” Bremner explains, “from working through problem-solving questions to assessment to fun games.”

This comprehensive nature meant teachers weren’t juggling multiple tools: they had everything in one platform. The school committed to systematic implementation and real teacher training, instead of just handing teachers another digital tool and hoping for the best. Their approach? Start with the youngest learners and build up.

Students learn the platform progressively from Kindergarten through Grade 8, teachers get ongoing support (not just a one-time training session) and most importantly, Mathletics becomes woven into daily instruction rather than treated as an add-on.

“We’ve been intentional about using Mathletics,” Bremner explains, “and so from Kindergarten up to Grade 8, we’re really training our children how to understand the platform, how to use it and how they can benefit from the resources.

When learning becomes play (without students realizing it)

Ask Bremner about gamification and he lights up. He’s watched something remarkable happen in his classroom over the years: students so absorbed in math challenges they forget they’re actually learning.

“Making things in a gamified way allows them to enjoy their learning and learning almost becomes secondary,” he shares. “And so, through that gamification, they learn that they can progress, and they can make mistakes, but they can still improve.”

For today’s digital-native students, this isn’t just nice to have – it’s speaking their language.

And nowhere is this more evident than with Live Mathletics, the program’s real-time math competitions where students can compete with peers from around the world.

 

These live challenges test students’ math fluency skills and reflexes, allowing whole schools, classes and individual learners to go head-to-head.

For Bremner’s class at this international school, it means they’re not just competing with classmates: they’re facing off against students from India, Pakistan, South Africa and Canada.

“[They] find ways of how they can get their answers in quicker and how they can compete with children around the world,” Bremner observes. “And so, it grows a global mindset not just within the classroom but on the platform that we’re using.”

The competitive element has genuinely engaged students. They enjoy customizing their avatars, working to beat their personal bests in timed challenges and tracking their progress against peers worldwide.

The immediate feedback and global competition keep them motivated to practice more, proving that when learning feels like play, students naturally want to keep improving.

The teacher’s game-changer: Data that actually helps

The engagement is just the beginning. For Bremner, the real value comes from how Mathletics helps him meet every student where they are.

Using the platform’s reporting features, Bremner tracks how students perform on activities and quests, gauging their responses against the school’s grading scale. But he doesn’t stop at assessment.

“What we do is build from that,” he explains, “build their understanding and make sure they’re [not just] working on topics being taught in class at that moment… so it’s not just about current learning, it’s about identifying students that need to be challenged and also children that need to be supported.”

This means advanced learners get extension activities that push them beyond the current curriculum, while struggling students receive targeted support exactly where they need it.

The school reinforces this differentiated approach with Mathletics’ printable booklets in their Response to Intervention (RTI) program.

The result? Every student gets what they need (challenge or support) based on real data, not guesswork.

Leadership that values what works

At First Baptist, administrative support comes with accountability. The principal’s approach is clear: she’s committed to providing Mathletics but expects to see it actively used in classrooms.

“She wants to make sure the teachers are intentional in its use,” Bremner explains, “and that it’s not just another resource that we just add to the list.”

This results-focused leadership means the school maintains accountability through:

• Usage monitoring via administrative accounts
• Activity tracking to measure engagement levels
• Regular review of minutes used and activities assigned
• Data-driven decisions about program effectiveness.

“I have an admin account and I look at how many activities are being assigned and how many minutes are being used,” Bremner shares. “We make sure that it’s actually being used for its true value.”

From one teacher’s journey to school-wide success

When Bremner first arrived at First Baptist, integrating a new platform while adapting to a new country and school felt challenging. Yet his perspective shifted dramatically through experience:

“And over time of using it, I grew to love it!” he reflects.

His transformation, from newcomer to the teacher who now guides colleagues through Mathletics implementation, mirrors First Baptist’s own six-year evolution.

Through Bremner’s experience, we see the key elements that drive success:

• Comprehensive training that unlocks features teachers didn’t know existed
• Engaged students participating because they want to, not because they must
• Meaningful data that informs teaching decisions and student support
• Committed leadership that backs investment with accountability and clear usage expectations
• Systematic progression building platform fluency from kindergarten through eighth grade
• Sustained support offering professional development beyond one-time training sessions.

Today, Bremner monitors usage data and provides the support he once needed himself, embodying the long-term approach First Baptist has built.

“When it comes to Mathletics, because we’ve embedded it within our culture of numeracy in the school, it’s allowed our teachers to feel confident in how they use it and our students to feel comfortable and confident with the platform.”

Bremner’s six-year journey shows exactly how sustainable maths success can happen – one teacher, one classroom, one school at a time!

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Kristina Gobetti*

Have you ever struggled with teaching statistics? Do you and your students share a sense of apprehension when data lessons appear on the scheme of work? You’re not alone. Anecdotally, many teachers tell me that statistics is one of the topics they like teaching the least, and I am no exception to this myself. In my mathematics degree I took the minimum number of statistics-related courses allowed following a very poor diet of data at school, and carried this negative association into my teaching. Looking back on my career in the classroom, I did not do a good job of teaching statistics, but having had the luxury of spending many years at Cambridge Mathematics immersed in research from excellent statistics teachers and education academics I now understand why!

So now of course, the question has been posed. Why is statistics hard to teach well? In part, I believe that it stems from viewing statistics through a mathematical lens – understandably, given that we are delivering it alongside quadratic equations, Pythagoras’ theorem, fractions, decimals and percentages. But while statistical analysis would not exist without the mathematical concepts and techniques underpinning it, we have a tendency within curricula to make the mathematical techniques the whole point, and reduce the statistical analysis part to an afterthought or an added extra. Students find the more subjective analysis hard, so it is tempting to make sure everyone can manage the techniques and then focus on the interpretation as something only the most able have time to spend on (although, there is always the additional temptation to move on to other, more properly ‘maths-y’ topics as soon as possible).

This approach is at odds with how education researchers suggest students should encounter statistical ideas. In the early 1990s, George Cobbⁱ and other researchers recommended that statistics should

• emphasise statistical thinking,
• include more real data,
• encourage the exploration of genuine statistical problems, and
• reduce emphasis on calculations and techniques.

Since then, much subsequent research has refined these recommendations to account for new technology tools and new ideas, but the core principles have remained the same. In much of my reading of education research, three ways of seeing or interacting with data keep appearing:

• Data modelling – the idea that data can be used to create models of the world in order to pose and answer questions
• Informal inference – the idea that data can be used to make predictions about something outside of the data itself with some attempt made to describe how likely the prediction is to be true
• Exploratory data analysis – the idea that data can be explored, manipulated and represented to identify and make visible patterns and associations that can be interpreted

In the abstract, these ways of seeing, while distinct, have a degree of overlap and all students may benefit from multiple experiences of all three approaches to data work from their very earliest encounters with data through to advanced level study.

Imagine the following classroom activity that could be given to very young students (e.g., in primary school). A class of students is given a list of snacks and treats and the students are asked to rank them on a scale of one to five based on how much they like each item. How could this data be worked with through each of the three approaches?

Firstly, we will consider data modelling. Students could be asked to plan a class party with a limited budget. They can buy some but not all of the items listed, and must decide what they should buy so that the maximum number of students get to have things they like. In this activity, students must create a model from the data that identifies those things they should buy more of, and those things they should buy least of, along with how many of each thing they should get – perhaps considering these quantities proportionally. This activity uses the data as a model but inevitably requires some assumptions and the creation of some principles. Is the goal to ensure everyone gets the thing they like most? Or is it to minimise the inclusion of the things students like least? What if everyone gets their favourite thing except one student who gets nothing they like?

Secondly, we will think about this as an activity in informal inference. Imagine a new student is joining the class and the class wants to make a welcome pack of a few treats for this student, but they don’t know which treats the student likes. Can they use the data to decide which five items an unknown student is most likely to choose? What if they know some small details about the student; would that additional information allow them to decide based on ‘similar’ students in the class? While the second part of this activity must be handled with a degree of sensitivity, it is an excellent primer for how purchasing algorithms, which are common in online shops, work.

Finally, we turn to exploratory data analysis. In this approach students are encouraged to look for patterns in the data, perhaps by creating representations. This approach may come from asking questions – e.g., do students who like one type of chocolate snacks rate the other chocolate snacks highly too? Is a certain brand of snack popular with everyone in the class? What is the least popular snack? Alternatively, the analysis may generate questions from patterns that are spotted – e.g. why do students seem to rate a certain snack highly? What are the common characteristics of the three most popular snacks?

Each of these approaches could be engaged in as separate and isolated activities, but there is also the scope to combine them, and use the results of one approach to inform another. For example, exploratory data analysis may usefully contribute both to model building and inference making, and support students’ justifications for their decisions in those activities. Similarly, data modelling activities can be extended into inferential tasks very easily, simply by shifting the use of the model from the population of the data (e.g., the students in the class it was collected from) to some secondary population (e.g., another class in the school, or as in the example, a new student joining the class).

Looking back on my time in the classroom, I wish that my understanding of these approaches and their importance for developing statistical reasoning skills in my students had been better. While not made explicit as important in many curricula, there are ample opportunities to embed these approaches and make them a fundamental part of the statistics teacher’s pedagogy.

Do you currently use any of these approaches in your lessons? Can you see where you might use them in the future? And how might you adapt activities to allow your students opportunities to engage in data modelling, informal inference and exploratory data analysis?

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Darren Macey*

Ground Picture/Shutterstock

Mathematics at A-level is going from strength to strength. Maths is the most popular subject choice, and further maths, which is a separate A-level course, has seen the most growth in uptake. Despite this, concerns still remain about the mathematical skills of young people who do not choose to study maths after they are 16.

Students in England who have passed GCSE maths at grade four or above, but who are not taking A-level or AS-level maths, are eligible to take a core maths qualification.

Core maths was introduced in 2014-15 to attempt to remedy a lack in mathematics education after 16. But the number of entries remains well short of what they could be. Many students who would benefit from maths after 16 are not taking this subject.

A 2010 report from the Nuffield Foundation found students in the UK lag their peers in other countries in participation in mathematics after the age of 16. Further research from the Royal Society and higher education charity AdvanceHE showed that as a consequence, many were not well prepared for the demands of their university courses or careers. Survey data has also found that over half of UK adults’ maths skills are low.

Many courses at university include mathematical or quantitative elements, but do not require AS or A-level maths for entry. These include psychology, geography, business and management, sociology, health sciences, biology, education and IT. When many students have not studied mathematics since GCSE, this results in a lack of fluency and confidence in using and applying it.

Core maths consolidates and builds on students’ mathematical understanding. The focus is on using and applying mathematics to authentic problems drawn from study, work and life. This includes understanding and using graphs, statistics and tools such as spreadsheets, as well as understanding risk and probability.

Core maths includes topics such as probability. EF Stock/Shutterstock

Take-up remains low despite incentives – schools receive an additional £900 in funding for each student who studies core maths. In 2025, 15,327 students took core maths – a 20% increase on 12,810 entries in 2024, which is very encouraging. However, research from the Royal Society in 2022 found that fewer than 10% of the number of A-level students who were not taking A-level mathematics had taken core maths, which will not have changed significantly even with the current numbers.

Increasing enrolment

There remains strong commitment from the government for increasing participation in mathematics after 16 in England through core maths. Many schools and colleges have embraced the subject, and universities have expressed support too.

However, a real incentive for teenagers to study this subject would be if it was rewarded in entry to university. Universities can allow students entry to a course with lower A-level grade profiles than normally required if they also passed core maths, for instance. But the number of universities making this kind of offer is low.

Schools and colleges need stronger signals from universities to induce them to offer students the opportunity to study for a core maths qualification, and to encourage their students to do so. Shifting today’s landscape to one where the vast majority of learners aged 16 to 19 in England are studying some form of mathematics which is relevant to their current and future interests and needs will require reform.

The Royal Society’s 2024 report on mathematical and data education sets out several reforms necessary to develop the mass mathematical, quantitative and data skills needed for the careers of the future. These include compulsory maths and data education in some form until 18. Extending the take up of core maths would be an excellent way to begin achieving this.

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Paul Glaister CBE*

Gorodenkoff/Shutterstock

In 2025, more young people than ever have opened their A-level results to find out how they did in their maths exam. Once again, maths has been the most popular A-level subject, with 112,138 entries in 2025.

This is up by more than 4% compared with 2024. Entries in further maths, an A-level that expands on the maths curriculum, have also risen – an increase of 7% since 2024, with over 19,000 entries this year.

As a professional mathematician this is pleasing news. Some of these students will be happily receiving confirmation of their place to study maths at university.

The joy I experienced when I discovered in my maths degree that many of the subjects I studied at school – chemistry, biology, physics and even music – are woven together by a mathematical fabric, is something I’ve never forgotten.

I’m excited by the idea that many young people are about to experience this for themselves. But I am concerned that fewer students will have the same opportunities in the future, as more maths departments are forced to downsize or close, and as we become more reliant on artificial intelligence.

There are a number of differences between studying maths at university compared with school. While this can be daunting at first, all of these differences underscore just how richly layered, deeply interconnected and vastly applicable maths is.

At university, not only do you learn beautiful formulas and powerful algorithms, but also grapple with why these formulas are true and dissect exactly what these algorithms are doing. This is the idea of the “proof”, which is not explored much at school and is something that can initially take students by surprise.

But proving why formulas are true and why algorithms work is an important and necessary step in being able discover new and exciting applications of the maths you’re studying.

Maths degrees involve finding out why mathematics works the way it does. Gorodenkoff/Shutterstock

A maths degree can lead to careers in finance, data science, AI, cybersecurity, quantum computing, ecology and climate modelling. But more importantly, maths is a beautifully creative subject, one that allows people to be immensely expressive in their scientific and artistic ideas.

A recent and stunning example of this is Hannah Cairo, who at just 17 disproved a 40-year old conjecture.

If there is a message I wish I knew when I started studying university mathematics it is this: maths is not just something to learn, but something to create. I’m continually amazed at how my students find new ways to solve problems that I first encountered over 20 years ago.

Accessiblity of maths degrees

But the question of going on to study maths at university is no longer just a matter of A-level grades. The recent and growing phenomenon of maths deserts – areas of the country where maths degrees are not offered – is making maths degrees less accessible, particularly for students outside of big cities.

Forthcoming research from The Campaign for Mathematical Sciences (CAMS), of which I am a supporter, shows that research-intensive, higher tariff universities – the ones that require higher grades to get in – took 66% of UK maths undergraduates in 2024, up from 56% in 2006.

This puts smaller departments in lower-tariff universities in danger of closure as enrolments drop. The CAMS research forecasts that an additional nine maths departments will have fewer than 50 enrolments in their degrees by 2035.

This cycle will further concentrate maths degrees in high tariff institutions, reinforcing stereotypes such as that only exceptionally gifted people should go on to study maths at university. This could also have severe consequences for teacher recruitment. The CAMS research also found that 25% of maths graduates from lower-tariff universities go into jobs in education, compared to 8% from higher tariff universities.

Maths in the age of AI

The growing capability and sophistication of AI is also putting pressure on maths departments

With Open AI’s claim that their recently released GPT-5 is like having “a team of PhD-level experts in your pocket”, the temptation to overly rely on AI poses further risks to the existence and quality of future maths degrees.

But the process of turning knowledge into wisdom and theory into application comes from the act of doing: doing calculations and forming logical and rigorous arguments. That is the key constituent of thinking clearly and creatively. It ensures students have ownership of their skills, capacities, and the work that they produce.

A data scientist will still require an in-depth working knowledge of the mathematical, algorithmic and statistical theory underpinning data science if they are going to be effective. The same for financial analysts, engineers and computer scientists.

The distinguished mathematician and computer scientist Leslie Lamport said that “coding is to programming what typing is to writing”. Just as you need to have some idea of what you are writing before you type it, you need to have some idea of the (mathematical) algorithm you are creating before you code it.

It is worth remembering that the early pioneers in AI – John McCarthy, Marvin Minsky, Claude Shannon, Alan Turing – all had degrees in mathematics. So we have every reason to expect that future breakthroughs in AI will come from people with mathematics degrees working creatively in interdisciplinary teams.

This is another great feature of maths: its versatility. It’s a subject that doesn’t just train you for a job but enables you to enjoy a rich and fulfilling career – one that can comprise many different jobs, in many different fields, over the course of a lifetime.

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Neil Saunders*

Mississippi’s reforms have led to significant gains in reading and math, despite the state being one of the lowest spenders per pupil in the U.S. Klaus Vedfelt/Getty Images

In a surprising turnaround, Mississippi, once ranked near the bottom of U.S. education standings, has dramatically improved its student literacy rates.

As of 2023, the state ranks among the top 20 for fourth grade reading, a significant leap from its 49th-place ranking in 2013. This transformation was driven by evidence-based policy reforms focused on early literacy and teacher development.

The rest of the country might want to take note.

That’s because Mississippi’s success offers a proven solution to the reading literacy crisis facing many states – a clear road map for closing early literacy gaps and improving reading outcomes nationwide.

As an expert on the economics of education, I believe the learning crisis is not just an educational issue. It’s also economic.

When students struggle, their academic performance declines. And that leads to lower test scores. Research shows that these declining scores are closely linked to reduced economic growth, as a less educated workforce hampers productivity and innovation.

The Mississippi approach

In 2013, Mississippi implemented a multifaceted strategy for enhancing kindergarten to third grade literacy. The Literacy-Based Promotion Act focuses on early literacy and teacher development. It includes teacher training in proven reading instruction methods and teacher coaching.

Relying on federally supported research from the Institute of Education Science, the state invested in phonics, fluency, vocabulary and reading comprehension. The law provided K-3 teachers with training and support to help students master reading by the end of third grade.

It includes provisions for reading coaches, parent communication, individual reading plans and other supportive measures. It also includes targeted support for struggling readers. Students repeat the third grade if they fail to meet reading standards.

The state also aligned its test to the NAEP, or National Assessment of Educational Progress, something which not all states do. Often referred to as “The Nation’s Report Card,” the NAEP is a nationwide assessment that measures student performance in various subjects.

Mississippi 4th graders’ reading improved the most from 2013 to 2022

According to federal data, fourth graders’ reading scores improved by nine points in Mississippi from 2013 to 2022. At the other end of the spectrum, Maryland fourth graders’ reading levels fell by 20 points over the same period.

Mississippi’s reforms have led to significant gains in reading and math, with fourth graders improving on national assessments.

I believe this is extremely important. That’s because early reading is a foundational skill that helps develop the ability to read at grade level by the end of third grade. It also leads to general academic success, graduating from high school prepared for college, and becoming productive adults less likely to fall into poverty.

Research by Noah Spencer, an economics doctoral student at the University of Toronto, shows that the Mississippi law boosted scores.

Students exposed to it from kindergarten to the third grade gained a 0.25 standard deviation improvement in reading scores. That is roughly equivalent to one year of academic progress in reading, according to educational benchmarks. This gain reflects significant strides in students’ literacy development over the course of a school year.

Another study has found an even greater impact attributed to grade retention in the third grade – it led to a huge increase in learning in English Language Arts by the sixth grade.

But the Mississippi law is not just about retention. Spencer found that grade retention explains only about 22% of the treatment effect. The rest is presumably due to the other components of the measure – namely, teacher training and coaching.

Other previous research supports these results across the country.

Adopting an early literacy policy improves elementary students’ reading achievement on important student assessments, with third grade retention and instructional support substantially enhancing English learners’ skills. The policy also increases test scores for students’ younger siblings, although it is not clear why.

Moreover, third grade retention programs immediately boost English Language Arts and math achievements into middle school without disciplinary incidents or negatively impacting student attendance.

These changes were achieved despite Mississippi being one of the lowest spenders per pupil in the U.S., proving that strategic investments in teacher development and early literacy can yield impressive results even with limited resources.

The global learning crisis

Mississippi’s success is timely. Millions of children globally struggle to read by age 10. It’s a crisis that has worsened after the COVID-19 pandemic.

Mississippi’s early literacy interventions show lasting impact and offer a potential solution for other regions facing similar challenges.

In 2024, only 31% of U.S. fourth grade students were proficient or above in reading, according to the NAEP, while 40% were below basic. Reading scores for fourth and eighth graders also dropped by five points compared with 2019, with averages lower than any year since 2005.

In 2013, Mississippi ranked 49th in fourth grade reading scores. Klaus Vedfelt/Getty Images

Mississippi’s literacy program provides a learning gain equal to a year of schooling. The program costs US$15 million annually – 0.2% of the state budget in 2023 – and $32 per student.

The learning gain associated with the Mississippi program is equal to about an extra quarter of a year. Since each year of schooling raises earnings by about 9%, then a quarter-year gain means that Mississippi students benefiting from the program will increase future earnings by 2.25% a year.

Based on typical high school graduate earnings, the average student can expect to earn an extra $1,000 per year for the rest of their life.

That is, for every dollar Mississippi spends, the state gains about $32 in additional lifetime earnings, offering substantial long-term economic benefits compared with the initial cost.

The Mississippi literacy project focuses on teaching at the right level, which focuses on assessing children’s actual learning levels and then tailoring instruction to meet them, rather than strictly following age- or grade-level curriculum.

Teaching at the right level and a scripted lessons plan are among the most effective strategies to address the global learning crisis. After the World Bank reviewed over 150 education programs in 2020, nearly half showed no learning benefit.

I believe Mississippi’s progress, despite being the second-poorest state, can serve as a wake-up call.

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Harry Anthony Patrinos*